XPM Prime Explorer symbol
XPMPrime Explorer

Block #75,528

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 5:00:34 PM Β· Difficulty 9.0135 Β· 6,741,347 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
3846fa4bcf38130aab670bf8d4b5181eaf4e9a62a30aa4ca27566cab8d5d6d23
View on Chainz β†—

Height

#75,528

Difficulty

9.013455

Transactions

1

Size

202 B

Version

2

Bits

090371ce

Nonce

19

Timestamp

7/21/2013, 5:00:34 PM

Confirmations

6,741,347

Mined by

⛏️ P2SHAL7xUNvqzokEQZCg3WuNjN3BhNg3sZr7s6

Merkle Root

4c4cc234d3ac622865b7f6f0155ecb071c9ebe9a9b1907ec782004851a62d12e
Transactions (1)
Coinbase4c4cc234d3ac62…2004851a62d12e
1 in β†’ 1 out12.2900 XPM110 B
AL7xUNvq…g3sZr7s6
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.549 Γ— 10⁹⁸(99-digit number)
25494021006679710930…46385333651991539841
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.549 Γ— 10⁹⁸(99-digit number)
25494021006679710930…46385333651991539841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.098 Γ— 10⁹⁸(99-digit number)
50988042013359421861…92770667303983079681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.019 Γ— 10⁹⁹(100-digit number)
10197608402671884372…85541334607966159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.039 Γ— 10⁹⁹(100-digit number)
20395216805343768744…71082669215932318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.079 Γ— 10⁹⁹(100-digit number)
40790433610687537488…42165338431864637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.158 Γ— 10⁹⁹(100-digit number)
81580867221375074977…84330676863729274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.631 Γ— 10¹⁰⁰(101-digit number)
16316173444275014995…68661353727458549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.263 Γ— 10¹⁰⁰(101-digit number)
32632346888550029991…37322707454917099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.526 Γ— 10¹⁰⁰(101-digit number)
65264693777100059982…74645414909834199041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,779,038 XPMΒ·at block #6,816,874 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy